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On controllability of fractional positive continuous-time linear systems with delay

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
Rocznik
Strony
29--51
Opis fizyczny
Bibliogr. 34 poz., wykr., wzory
Twórcy
autor
  • Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
  • Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
  • [1] A. Abdelhakim and J. Tenreiro Machado: A critical analysis of the conformable derivative, Nonlinear Dynamics, 95 (2019), 3063-3073, DOI: 10.1007/s11071-018-04741-5.
  • [2] K. Balachandran, Y. Zhou and J. Kokila: Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 3508-3520, DOI: 10.1016/j.cnsns.2011.12.018.
  • [3] K. Balachandran, J. Kokila, and J. J. Trujillo: Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Apllications, 64 (2012), 3037-3045, DOI: 10.1016/j.camwa.2012.01.071.
  • [4] P. Duch: Optimization of numerical algorithms using differential equations of integer and incomplete orders, Doctoral dissertation, Lodz University of Technology, 2014 (in Polish).
  • [5] C. Guiver, D. Hodgson and S. Townley: Positive state controllability of positive linear systems. Systems and Control Letters, 65 (2014), 23-29, DOI: 10.1016/j.sysconle.2013.12.002.
  • [6] R. E. Gutierrez, J. M. Rosario and J. T. Machado: Fractional order calculus: Basic concepts and engineering applications, Mathematical Problems in Engineering, 2010 Article ID 375858, DOI: 10.1155/2010/375858.
  • [7] T. Kaczorek: Positive 1D and 2D Systems, Communications and Control Engineering, Springer, London 2002.
  • [8] T. Kaczorek: Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science, 18 (2008), 223-228, DOI: 10.2478/v10006-008-0020-0.
  • [9] T. Kaczorek: Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences, 58 (2010), 453-458, DOI: 10.2478/v10175-010-0043-1.
  • [10] T. Kaczorek: Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Science, 411, 2011.
  • [11] T. Kaczorek: Constructability and observability of standard and positive electrical circuits, Electrical Review, 89 (2013), 132-136.
  • [12] T. Kaczorek: An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences, 62 (2014), 227-231, DOI: 10.2478/bpasts-2014-0022.
  • [13] T. Kaczorek: Minimum energy control of fractional positive continuoustime linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science, 24 (2014), 335-340, DOI: 10.2478/amcs-2014-0025.
  • [14] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits, Springer, Studies in Systems, Decision and Control, 13 2015.
  • [15] T. Kaczorek: A class of positive and stable time-varying electrical circuits, Electrical Review, 91 (2015), 121-124. DOI: 10.15199/48.2015.05.29.
  • [16] T. Kaczorek: Computation of transition matrices of positive linear electrical circuits, BUSES - Technology, Operation, Transport Systems, 24 (2019), 179-184, DOI: 10.24136/atest.2019.147.
  • [17] A. A. Kilbas, H.M. Srivastava and J. J. Trujillo: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, 2006.
  • [18] J. Klamka: Controllability of Dynamical Systems, Kluwer Academic Publishers, 1991.
  • [19] T. J. Machado,V. Kiryakova and F. Mainardi: Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, 6 (2011), 1140-1153, DOI: 10.1016/j.cnsns.2010.05.027.
  • [20] K. S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Calculus, Villey, 1993.
  • [21] A. Monje, Y. Chen, B. M. Viagre, D. Xue and V. Feliu: Fractional-order Systems and Controls. Fundamentals and Applications, Springer-Verlag, 2010.
  • [22] K. Nishimoto: Fractional Calculus: Integrations and Differentiations of Arbitrary Order, University of New Haven Press, 1989.
  • [23] K. B. Oldham and J. Spanier: The Fractional Calculus, Academic Press, 1974.
  • [24] I. Podlubny: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, In: Mathematics in Science and Engineering, Academic Press, 1999.
  • [25] S. G. Samko, A. A. Kilbas and O. I. Marichev: Fractional Integrals and Derivatives: Theory and Applications, Gordan and Breach Science Publishers, 1993.
  • [26] J. Sabatier, O. P. Agrawal and J. A. Tenreiro Machado: Advances in Fractional Calculus, In: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, 2007.
  • [27] B. Sikora: Controllability of time-delay fractional systems with and without constraints, IET Control Theory & Applications, 10 (2016), 1-8, DOI: 10.1049/iet-cta.2015.0935.
  • [28] B. Sikora: Controllability criteria for time-delay fractional systems with a retarded state, International Journal of Applied Mathematics and Computer Science, 26 (2016), 521-531, DOI: 10.1515/amcs-2016-0036.
  • [29] B. Sikora and J. Klamka: Constrained controllability of fractional linear systems with delays in control, Systems and Control Letters, 106 (2017), 9-15, DOI: 10.1016/j.sysconle.2017.04.013.
  • [30] B. Sikora and J. Klamka: Cone-type constrained relative controllability of semilinear fractional systems with delays, Kybernetika, 53 (2017), 370-381, DOI: 10.14736/kyb-2017-2-0370.
  • [31] B. Sikora: On application of Rothe’s fixed point theorem to study the controllability of fractional semilinear systems with delays, Kybernetika, 55 (2019), 675-689, DOI: 10.14736/kyb-2019-4-0675.
  • [32] T. Schanbacher: Aspects of positivity in control theory, SIAM J. Control and Optimization, 27 (1989), 457-475.
  • [33] B. Trzasko: Reachability and controllability of positive fractional discretetime systems with delay, Journal of Automation Mobile Robotics and Intelligent Systems, 2 (2008), 43-47.
  • [34] J. Wei: The controllability of fractional control systems with control delay, Computers and Mathematics with Applications, 64 (2012), 3153-3159, DOI: 10.1016/j.camwa.2012.02.065
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3e14df51-7f25-4454-99f9-98a297bce8e9
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